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Side of a Polygon — Definition, Examples & Properties

Side of a Polygon

Any of the line segments that make up a polygon. For example, a triangle has three sides.

 

 

 

See also

Vertex, interior of a polygon

Worked Example

Problem: A regular hexagon has a perimeter of 42 cm. How many sides does it have, and what is the length of each side?
Step 1: Identify the polygon. A hexagon has 6 sides.
n=6n = 6
Step 2: Since the hexagon is regular, all 6 sides are equal in length. The perimeter is the sum of all side lengths.
P=n×sP = n \times s
Step 3: Substitute the known values and solve for the side length.
42=6×s  ⟹  s=426=7 cm42 = 6 \times s \implies s = \frac{42}{6} = 7 \text{ cm}
Answer: The hexagon has 6 sides, each measuring 7 cm.

Another Example

Problem: A quadrilateral has sides of lengths 5 cm, 8 cm, 6 cm, and 11 cm. Find its perimeter.
Step 1: Count the sides. A quadrilateral has 4 sides.
n=4n = 4
Step 2: Add all four side lengths to find the perimeter.
P=5+8+6+11=30 cmP = 5 + 8 + 6 + 11 = 30 \text{ cm}
Answer: The perimeter of the quadrilateral is 30 cm.

Frequently Asked Questions

How many sides does each type of polygon have?
A triangle has 3 sides, a quadrilateral has 4, a pentagon has 5, a hexagon has 6, a heptagon has 7, an octagon has 8, a nonagon has 9, and a decagon has 10. In general, an n-gon has n sides. The number of sides always equals the number of vertices.
Is a side the same as an edge?
For two-dimensional polygons, "side" and "edge" mean the same thing — both refer to the line segments forming the boundary. The term "edge" is more commonly used for three-dimensional shapes (like the edges of a cube), while "side" is the standard term for polygons.

Side vs. Diagonal

A side connects two consecutive (adjacent) vertices of a polygon, forming part of its boundary. A diagonal connects two non-adjacent vertices and lies inside the polygon. For example, a rectangle has 4 sides but 2 diagonals. Every polygon has the same number of sides as vertices, but the number of diagonals grows much faster as the polygon gains more sides.

Why It Matters

Sides are the most fundamental building blocks of any polygon. Knowing the number of sides tells you the polygon's name, determines how many vertices and interior angles it has, and lets you calculate its perimeter by summing all side lengths. Many formulas in geometry — including the interior angle sum formula (n−2)×180°(n - 2) \times 180° — depend directly on the number of sides nn.

Common Mistakes

Mistake: Confusing sides with diagonals when counting line segments in a polygon.
Correction: Sides only connect consecutive vertices along the boundary. Any line segment connecting two non-adjacent vertices is a diagonal, not a side.
Mistake: Assuming all sides of a polygon are equal in length.
Correction: Only regular polygons have all sides equal. Most polygons are irregular, meaning their sides can have different lengths. Always check whether a problem specifies a regular polygon before assuming equal sides.

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